Possible bars to employment--where to apply?

I will preface this post by apologizing for its length.

On Friday, I am scheduled to go to the DMV and test for my CDL. The next obvious step is to find a trucking job. Werner sent me a pre-hire last month, and then last week told me they had nothing for me, but I could re-apply in two months. I don't have two months to wait around, so I must look for another job. However, there are some things that might hold me back:

1. I have spent much of the last three years unemployed (though I was a full-time student for almost half of that time and supporting myself with a housing allowance from the VA, and my ten-year work history includes my time in the Navy).
2. I have been fired from a job within the past six months.
3. I had a reckless-driving conviction in September 2002 (I might be able to have it removed, and I only have one point on my record).

With those in mind, I have some other preferences in a job:

1. I want to run flatbeds, without having to "prove" myself in a dry-van or a reefer first.
2. I'll consider dry-vans or reefers if all flatbed options are exhausted.
3. Unless all other options are exhausted, I do not want to run teams.
4. I currently live in central California, and though I plan to move no later than the end of next year, it isn't feasible right now.
5. I'd like to avoid the hassles associated with passports and TWIC cards, if possible.
6. I'd rather starve to death than work for C.R. England.

Can anyone suggest a decent company for me to look into?

 

I know that if one has been employed over X amount of days, some companies want letters stating why. Might I have to do something along those lines?

I've looked into Hunt before, but what really worries me is that their closest terminals are in Phoenix and SLC. I'll give 'em a call come Monday and see if that won't be a huge issue.

 

It's still there. The incident occurred in September 2002. I was able to get my CDL permit without any hassle, though.